Sentence examples for boundedness of the sequence from inspiring English sources
Furthermore, by utilizing the mathematical induction, a sufficient condition is established to ensure the asymptotic boundedness of the sequence of the error covariance.
The boundedness of the sequence { x n } yields.
The boundedness of the sequence { x n } follows.
It remains to prove the boundedness of the sequence in.
By boundedness of the sequence and by, we have (3.21).
Now, we show the boundedness of the sequence ({x_{n}}).
Notice the boundedness of the sequences { x n } and { W n x n }.
The next lemma will be a useful tool to obtain the boundedness of the sequences generated by the algorithms and also to obtain the convergence of the whole sequence to the solution.
By virtue of ξ n → 0 (as n → ∞ ) and the boundedness of the sequences { f ( x n ) } and { B x n }, we firstly observe that lim n → ∞ ∥ y n − x n ∥ = lim n → ∞ ξ n ∥ σ f ( x n ) − B x n ∥ = 0, and lim n → ∞ ∥ z n − U y n ∥ = lim n → ∞ ( 1 − δ ) ξ n δ ∥ σ f ( x n ) − B x n ∥ = 0. Next, we estimate ∥ z n + 1 − z n ∥.
To prove the boundedness of the generated sequence ({x^{k}}), we assume that the algorithm generates an infinite sequence for simple.
We investigate the boundedness of the iteration sequence generated by smoothing methods under the P0 assumption.
